Problem: Simplify the following expression: $ n = \dfrac{-3}{5} - \dfrac{t - 1}{6t + 1} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6t + 1}{6t + 1}$ $ \dfrac{-3}{5} \times \dfrac{6t + 1}{6t + 1} = \dfrac{-18t - 3}{30t + 5} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{t - 1}{6t + 1} \times \dfrac{5}{5} = \dfrac{5t - 5}{30t + 5} $ Therefore $ n = \dfrac{-18t - 3}{30t + 5} - \dfrac{5t - 5}{30t + 5} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{-18t - 3 - (5t - 5) }{30t + 5} $ Distribute the negative sign: $n = \dfrac{-18t - 3 - 5t + 5}{30t + 5}$ $n = \dfrac{-23t + 2}{30t + 5}$